Question

What are the zeros of the polynomial function f(x) = x3 + 2x2 − 24x?

Answer 1

You may notice that all of the terms have a common factor: $x$. So, let's take the $x$ out of all the terms. This gives us:

$x(x^2 + 2x - 24) = 0$

Using the Zero Product Property, we can say that both $x = 0$ and $x^2 + 2x - 24 = 0$.

Let's solve both. $x = 0$ is obvious, but we still need to solve our other term:

$x^2 + 2x - 24 = 0$

• Set up

$(x + 6)(x - 4) = 0$

• Factor

$x = -6, 4$

• Apply the Zero Product Property

Our answer is x = -6, 0, 4.